January 2013

Edexcel Award in Algebra

Level 3 Practice Paper Time: 2 hours

You must have: Ruler graduated in centimetres and millimetres, pen, HB pencil, eraser, pair of compasses.

Instructions

Use black ink or ball-point pen.

Answer all questions.

Answer the questions in the shaded boxes provided. – there may be more space than you need.

Write your answer on the answer line where shown. Information

The total mark for this paper is 90.

The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice

Read each question carefully before you start to answer it.

Keep an eye on the time.

Try to answer every question.

Check your answers if you have time at the end.

This publication may be reproduced only in accordance with

Edexcel Limited copyright policy.

©2012 Edexcel Limited.

2

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages of your working.

1 (a) Simplify (p4)−3

................................

(1)

(b) Simplify t 2

3

× t

................................

(1)

(c) 2x−2

(3x2 − x) = a + bx

n for all values of x.

Find the value of a, the value of b and the value of n.

a = ...........................

b = ...........................

n = ...........................

(3)

(Total for Question 1 is 5 marks)

3

2 (a) Expand and simplify (4x − 1)(4x + 1)

.........................................................

(2)

(b) Solve the equation (5x − 1)2 = 4

.........................................................

(3)

(Total for Question 2 is 5 marks)

4

3 Write down the 4 inequalities that are satisfied by all points in the shaded region.

(Total for Question 3 is 4 marks)

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 0 x

y

5

4 Here is part of the graph of y = tan x°.

Use the graph to find a solution of the equation 2 tan x° = 5

................................

(Total for Question 4 is 2 marks)

2

4

6

8

10

−2

−4

−6

−8

−10

20 40 60 80 100 −20 −40 −60 −80 −100 x

y

O

6

5 (a) Solve

x² − 2x − 4 = 0

Give your solutions in surd form.

.........................................................

(2)

(b) Solve

x² − 2x − 4 0

Give your solutions in surd form.

.........................................................

(2)

(Total for Question 5 is 4 marks)

7

6 (a) The equation px2 − 4px + 8 = 0 has 2 equal roots.

(i) Find the value of p.

(ii) For this value of p, solve the equation.

(4)

(b) qx2 + 3qx + 12 = 0 is 1.5

The product of the roots of this equation is 1.5

(i) Find the value of q.

(ii) Find the sum of the roots.

(3)

(Total for Question 6 is 7 marks)

8

7 (a) Factorise x2 − 4x − 12

.........................................................

(2)

(b) Simplify fully 9

32

2

x

xx ÷

2)3(

62

x

x

................................

(4)

(Total for Question 7 is 6 marks)

9

8 The straight line L1 passes through the points P and Q with coordinates (1, 5) and (3, 2)

respectively.

The line L2 is perpendicular to the line L1 and passes through the point P.

Find the equation of the line L2

Give your answer in the form y = mx + c

................................

(Total for Question 8 is 4 marks)

10

9 a = n

cp

(a) Make c the subject of the formula.

...............................

(3)

y = x

x

2

1

(b) Make x the subject of the formula.

................................

(3)

(Total for Question 9 is 6 marks)

11

10 (a) Simplify 5

5

15

(2)

(b) Write 2

1

+

8

1

in the form

b

a2 where a and b are integers.

................................

(4)

(Total for Question 10 is 6 marks)

12

11 Here is a sketch graph of y = f(x).

On the axes below, sketch the graph of y = −2f(x).

On your sketch, show the coordinates of any points where the curve intersects the x-axis and of any

turning points.

(Total for Question 11 is 3 marks)

x

y

(3, −2)

6 x

y

×

O

O

13

12 Here is part of a distance–time graph of a bus.

(a) Calculate the speed of the bus during the first 20 seconds.

.......................... m/s

(2)

After 20 seconds the bus travels at a speed of 5.5 m/s for a further 40 seconds.

(b) Show this information on the distance–time graph.

(2)

(Total for Question 12 is 4 marks)

200

400

600

20 40 60 80 0 Time (s)

Distance (m)

0

14

13 The first term of an arithmetic series is 5

The common difference of the same series is 2.5

(a) Work out the 100th term of this series.

................................

(2)

The common difference of a different arithmetic series is −5

The sum of the first 40 terms of this arithmetic series is 6100

(b) Work out the first term of this series.

................................

(3)

(Total for Question 13 is 5 marks)

15

14 y is inversely proportional to the square root of x.

When x = 64, y = 2

(a) Find a formula for y in terms of x.

(3)

(b) Calculate the value of x when y = 80

................................

(2)

(Total for Question 14 is 5 marks)

16

15 A curve has equation y = 2

1

x.

(a) Find the coordinates of the point where the graph of y = 2

1

x intersects the y-axis.

................................

(1)

The graph of y = 2

1

x has two asymptotes.

(b) Find an equation of the asymptote to the curve which is parallel to

(i) the x-axis,

(ii) the y-axis.

................................

................................

(2)

17

(c) On the axes below, sketch the graph of y = 2

1

x.

Show the asymptotes and label the points where the curve crosses the y-axis.

(2)

(Total for Question 15 is 5 marks)

x

y

18

16 (a) Complete the table of values for y = 2x

x 0 1 2 3 4 5

y

(2)

(b) Use the trapezium rule to find an estimate of the area of the region under the curve with

equation y = 2x and between x = 0 and x = 5

Use 5 strips of equal width.

(3)

(Total for Question 16 is 5 marks)

19

17 On the grid, draw the graph of (x − 2)2 + (y + 1)

2 = 9

(Total for Question 17 is 3 marks)

1

2

3

4

5

6

7

−1

−2

−3

−4

−5

−6

−7

1 2 3 4 5 6 7 −1 −2 −3 −4 −5 −6 −7 O x

y

20

18 A car accelerates from rest at 5 m/s2 for 3 seconds , travels with constant speed for 5 seconds and

decelerates at 2 m/s2 for 2 seconds.

(a) Draw a speed-time graph to show this information.

(3)

(b) Find the total distance travelled by the car in the 10 seconds.

................................

(3)

(Total for Question 18 is 6 marks)

21

19 Solve the simultaneous equations

x + y = 6

y = 2x2 + 4x + 3

.........................................................

(Total for Question 19 is 5 marks)

TOTAL FOR PAPER IS 90 MARKS